Sparse systems and algorithmic equidimensional decomposition

Fuente: arXiv
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Auteurs principaux: Herrero, Maria Isabel, Jeronimo, Gabriela, Sabia, Juan
Format: Preprint
Publié: 2025
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author Herrero, Maria Isabel
Jeronimo, Gabriela
Sabia, Juan
author_facet Herrero, Maria Isabel
Jeronimo, Gabriela
Sabia, Juan
contents We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved.
format Preprint
id arxiv_https___arxiv_org_abs_2505_08097
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sparse systems and algorithmic equidimensional decomposition
Herrero, Maria Isabel
Jeronimo, Gabriela
Sabia, Juan
Algebraic Geometry
13P15, 14Q20, 68W30
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved.
title Sparse systems and algorithmic equidimensional decomposition
topic Algebraic Geometry
13P15, 14Q20, 68W30
url https://arxiv.org/abs/2505.08097